Material is stretching when using Edge Loop
The reason for the difference is the top-to-bottom interpolation of normals, inside the rectangular faces. This illustration shows 2 standard cylinders. They are both shaded smooth, but the one on the right has Autosmooth switched on.

When smooth-shaded,the normal at some shading-point inside a polygonal face is an interpolation of the vertex-normals at its corners. Those, in turn, are a (sometimes weighted) average of the normals of the whole-faces which the vertices help to define.
As you can see on the left, in pure smooth shading, because of the top and bottom faces, those vertex-normals have a Z component, looking up and down. The interpolation between these gives the geometrically cylindrical surface a somewhat spherical field of interpolated normals. Strictly speaking,this actually produces the inaccurate reflection.
On the right, switching on Autosmooth introduces the influence of per face-vertex normals. Autosmooth sets a face-angle threshold for interpolation. Below the threshold, faces are interpolated, above it they are split. The top and bottom face-normals no longer influence the radial normals, which are then aligned to the geometry. In an orthographic view, like this one, the cylinder reflects only its own height in the environment. In perspective, the reflection is more like a real cylinder's, than the one on the left.
There's a similar result from introducing edge-loops - they cut the top and bottom faces out of the interpolation of radial normals, for a truer cylindrical reflection.